1. Jan 4, 2008Aharon Levy - Hosza seminar1 Gluons in the proton and exclusive hard diffraction Aharon Levy Tel Aviv University and MPI Introduction soft, hard interactions gluons data on exclusive vector meson electroproduction sizes of gluon cloud sizes of photon configurations effective Pomeron trajectory comparison to theory

2. Jan 4, 2008Aharon Levy - Hosza seminar2

3. Jan 4, 2008Aharon Levy - Hosza seminar3 LHeC

4. Jan 4, 2008Aharon Levy - Hosza seminar4 Deep Inelastic kinematics Spin [20 fb -1 /point]

5. Jan 4, 2008Aharon Levy - Hosza seminar5 McAllister, HofstadterEe=188 MeVr min =0.4 fm Bloom et al. 10 GeV 0.05 fm CERN, FNAL fixed target 500 GeV 0.007 fm HERA 50 TeV 0.0007 fm HERA Kinematics E e =27.5 GeV E P =920 GeV s=(k+P) 2 = (320 GeV) 2 e p r b Transverse distance scale: Impact parameter : where t is the square of the 4-momentum transferred to the proton

6. Jan 4, 2008Aharon Levy - Hosza seminar6 Proton  momentum frame Partons frozen during time of interaction. Virtual photon samples the quark distribution. Assume that partons form incoherent beam. The parton density distributions are meant to be universal quantities.

7. Jan 4, 2008Aharon Levy - Hosza seminar7 Proton rest-frame e p r b Photon fluctuates into,, ….. states, which interact with the proton. r large  interaction soft, r small  interaction hard. soft and hard – studied by W (or x~1/W 2 ) dependence of the cross section.

8. Jan 4, 2008Aharon Levy - Hosza seminar8 high energy behavior  tot  s 0.08 Donnachie and Lanshoff – universal behavior of total hadron-hadron cross section : soft

9. Jan 4, 2008Aharon Levy - Hosza seminar9 Regge trajectories IP - Pomeron

10. Jan 4, 2008Aharon Levy - Hosza seminar10 hard The rise of F 2 with decreasing x is strongly dependent on Q 2. DIS: at small x

11. Jan 4, 2008Aharon Levy - Hosza seminar11 Below Q 2  0.5 GeV 2, see same energy dependence as observed in hadron- hadron interactions. Start to resolve the partons.   s 0.08 soft  hard

12. Jan 4, 2008Aharon Levy - Hosza seminar12 QCD based fits can follow the data accurately, yield parton densities. BUT: many free parameters (18-30) (only know how parton densities evolve) form of parameterisation fixed by hand (not given by theory) F 2  parton densities.  * ‘sees’ partons. parton density increases with decreasing x.

13. Jan 4, 2008Aharon Levy - Hosza seminar13 From Pumplin, DIS05 There are signs that DGLAP (Q 2 evolution) may be in trouble at small x (negative gluons, high  2 for fits). Need better data to test whether our parton densities are reasonable. The structure function F L will provide an important test. all is not well … Can also get information on gluon density from exclusive hard processes.

14. Jan 4, 2008Aharon Levy - Hosza seminar14 Exclusive VM electroproduction (V 0 =   DVCS)

15. Jan 4, 2008Aharon Levy - Hosza seminar15 soft to hard transition IP ‘soft’ ‘hard’ gg Expect  to increase from soft (~0.2, from ‘soft Pomeron’ value) to hard (~0.8, from xg(x,Q 2 ) 2 ) Expect b to decrease from soft (~10 GeV -2 ) to hard (~4-5 GeV -2 )

16. Jan 4, 2008Aharon Levy - Hosza seminar16 ingredients Use QED for photon wave function. Study properties of V-meson wf and the gluon density in the proton.

17. Jan 4, 2008Aharon Levy - Hosza seminar17 Mass distributions

18. Jan 4, 2008Aharon Levy - Hosza seminar18 Photoproduction process becomes hard as scale (mass) becomes larger.

19. Jan 4, 2008Aharon Levy - Hosza seminar19  (W) – ρ 0 Fix mass – change Q 2

20. Jan 4, 2008Aharon Levy - Hosza seminar20  (W) - , J/ , 

21. Jan 4, 2008Aharon Levy - Hosza seminar21  (Q 2 +M 2 ) - VM

22. Jan 4, 2008Aharon Levy - Hosza seminar22  (Q 2 ) Fit to whole Q 2 range gives bad  2 /df (~70) VMncomments ρ2.44±0.09Q 2 >10 GeV 2  2.75±0.13 ±0.07 Q 2 >10 GeV 2 J/  2.486±0.080 ±0.068 All Q 2  1.54±0.09 ±0.04 Q 2 >3 GeV 2 101 Q 2 (GeV 2 )

23. Jan 4, 2008Aharon Levy - Hosza seminar23 b(Q 2 ) – ρ 0,  Fit:

24. Jan 4, 2008Aharon Levy - Hosza seminar24 b(Q 2 +M 2 ) - VM ‘hard’ gg

25. Jan 4, 2008Aharon Levy - Hosza seminar25 Frankfurt - Strikman Kornelija Passek-Kumaricki - EDS07 DVCS

26. Jan 4, 2008Aharon Levy - Hosza seminar26 Information on  L and  T Use  0 decay angular distribution to get r 04 00 density matrix element  - ratio of longitudinal- to transverse- photon fluxes ( = 0.996) using SCHC

27. Jan 4, 2008Aharon Levy - Hosza seminar27 R=  L /  T (Q 2 ) When r 00 04 close to 1, error on R large and asymmetric  advantageous to use r 00 04 rather than R.

28. Jan 4, 2008Aharon Levy - Hosza seminar28 Photon configuration - sizes small k T large k T large config. small config.  T : large size small size strong color forces color screening large cross section small cross section  *:  * T,  * L  * T – both sizes,  * L – small size Light VM: transverse size of ~ size of proton Heavy VM: size small  cross section much smaller (color transparency) but due to small size (scale given by mass of VM) ‘see’ gluons in the proton   ~ (xg) 2  large 

29. Jan 4, 2008Aharon Levy - Hosza seminar29  L /  tot (W)   L and  T same W dependence  L  in small configuration  T  in small and large configurations small configuration  steep W dep large configuration  slow W dep  large configuration is suppressed

30. Jan 4, 2008Aharon Levy - Hosza seminar30  L /  tot (t)  size of  * L   * T  large configuration suppressed

31. Jan 4, 2008Aharon Levy - Hosza seminar31  (W) - DVCS Final state  is real   T using SCHC  initial  * is  * T but W dep of  steep  large  * T configurations suppressed

32. Jan 4, 2008Aharon Levy - Hosza seminar32 Effective Pomeron trajectory ρ 0 photoproduction Get effective Pomeron trajectory from d  /dt(W) at fixed t Regge:

33. Jan 4, 2008Aharon Levy - Hosza seminar33 Effective Pomeron trajectory ρ 0 electroproduction

34. Jan 4, 2008Aharon Levy - Hosza seminar34 Comparison to theory All theories use dipole picture Use QED for photon wave function Use models for VM wave function – usually take a Gaussian shape Use gluon density in the proton Some use saturation model, others take sum of nonperturbative + pQCD calculation, and some just start at higher Q 2 Most work in configuration space, MRT works in momentum space. Configuration space – puts emphasis on VM wave function. Momentum space – on the gluon distribution. W dependence – information on the gluon Q 2 and R – properties of the wave function

35. Jan 4, 2008Aharon Levy - Hosza seminar35 ρ 0 data - Comparison to theory Martin-Ryskin-Teubner (MRT) – work in momentum space, use parton-hadron duality, put emphasis on gluon density determination. Phys. Rev. D 62, 014022 (2000). Forshaw-Sandapen-Shaw (FSS) – improved understanding of VM wf. Try Gaussian and DGKP (2- dim Gaussian with light-cone variables). Phys. Rev. D 69, 094013 (2004). Kowalski-Motyka-Watt (KMW) – add impact parameter dependence, Q 2 evolution – DGLAP. Phys. Rev. D 74, 074016 (2006). Dosch-Ferreira (DF) – focusing on the dipole cross section using Wilson loops. Use soft+hard Pomeron for an effective evolution. Eur. Phys. J. C 51, 83 (2007).

36. Jan 4, 2008Aharon Levy - Hosza seminar36 Q2Q2 KMW – good for Q 2 >2GeV 2 miss Q 2 =0 DF – miss most Q 2 FSS – Gauss better than DGKP

37. Jan 4, 2008Aharon Levy - Hosza seminar37 Q2Q2 Data seem to prefer MRST99 and CTEQ6.5M

38. Jan 4, 2008Aharon Levy - Hosza seminar38 W dependence KMW - close FSS: Sat-Gauss – right W-dep. wrong norm. MRT: CTEQ6.5M – slightly better in W-dep.

39. Jan 4, 2008Aharon Levy - Hosza seminar39  L /  tot (Q 2 )

40. Jan 4, 2008Aharon Levy - Hosza seminar40  L /  tot (W) All models have mild W dependence. None describes all kinematic regions.

41. Jan 4, 2008Aharon Levy - Hosza seminar41 Summary and conclusions HERA data shows transition from soft to hard interactions. The cross section is rising with W and its logarithmic derivative in W, , increases with Q 2. The exponential slope of the t distribution decreases with Q 2 and levels off at about b = 5 GeV -2. Transverse size of gluon density (0.6 fm) inside the charge radius of the proton (0.8 fm). The ratio of cross sections induced by longitudinally and transversely polarised virtual photons increases with Q 2, but is independent of W and t. The large configurations of the transversely polarised photon are suppressed. The effective Pomeron trajectory has a larger intercept and smaller slope than those extracted from soft interactions. All these features are compatible with expectations of perturbative QCD. None of the models which have been compared to the measurements are able to reproduce all the features of the data. Precision measurements of exclusive vector meson electroproduction can help determine the gluon density in the proton.